Challenge · Medium problem

Two circles are externally tangent to each other, and both are tangent to a line $\ell$ on the same side of $\ell$. The smaller circle has radius $2$ and the larger circle has radius $8$. A third circle is nestled in the curvilinear region bounded by $\ell$ and the two given circles, tangent to $\ell$ and to each of the two circles. Find the radius of this third circle.

Express your answer as a common fraction.